A) \[a\sqrt{3}\]
B) \[a\]
C) \[3a\]
D) \[{{a}^{2}}\]
Correct Answer: A
Solution :
In equilateral triangle all sides are equal. In\[\Delta ADB\] AD is a altitude so, In\[\Delta ADB\].\[\angle ADB\]is a right angle \[{{(AB)}^{2}}={{(AD)}^{2}}+{{(BD)}^{2}}\] \[{{(AD)}^{2}}={{(AB)}^{2}}-{{(BD)}^{2}}\] \[{{(AD)}^{2}}={{(2a)}^{2}}-{{(a)}^{2}}\] \[{{(AD)}^{2}}=4{{a}^{2}}-{{a}^{2}}\] \[{{(AD)}^{2}}=3{{a}^{2}},\] \[AD=\sqrt{3{{a}^{2}}}=a\sqrt{3}\]You need to login to perform this action.
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